DLMF:18.7.E10 (Q5578)

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DLMF:18.7.E10
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    Statements

    Defining formula
    P n * ⁡ ( x ) = P n ⁡ ( 2 ⁢ x - 1 ) . shifted-spherical-Legendre-polynomial-s 𝑛 𝑥 Legendre-spherical-polynomial 𝑛 2 𝑥 1 {\displaystyle{\displaystyle P^{*}_{n}\left(x\right)=P_{n}\left(2x-1\right).}}
    0 references
    DLMF id
    DLMF:18.7.E10
    0 references
    Symbols used
    Q10920
    Defining formula
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2aadec
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    Q11749
    Defining formula
    P n * ⁡ ( x ) shifted-spherical-Legendre-polynomial-s 𝑛 𝑥 {\displaystyle{\displaystyle P^{*}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r11.m2adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1idec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1idec
    0 references
     
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